OP said nitrites were 5ppm not 0.
Op is your light off? No way should you be having algae issues so soon.
If your nitrite is 5, your nitrates will look large but it’s a false reading, until your nitrites read 0 your nitrates will read in the test higher than there are, it’s just the way the nitrate test works, so don’t stress too much over that.
once your nitrites start dropping they drop fast, not sure how you cycled exactly but it sounds you are not far off, maybe try a different test for nitrites a lot of people don’t get on with api tests, salifert is good for nitrites.
Sorry but have to say, you need a lot of patience in this hobby, within a matter of days you have lost it over noise in the tank now the cycle, I would take a deep breath and really enjoy the slow peace of this hobby because rushing it, things go bad really quickly.